First, why would you use an MMA pin over an Aikido pin? In a situation like MMA, body to body pins (mount, side mount, north south, rear mount etc.) work better. This is because they allow you to hold your opponent with the whole of your body. This allows you to directly (as opposed to indirectly; through an arm) use your body weight, structure, and force on your attackers body. This will make him tire, making his breathing irregular, and cause him to use muscular force to escape your hold, while you essentially rest your body weight on him.

Second, why would you apply an Aikido pin? In a non-sport situation you may have to look for other attackers, assess the terrain, call for help, make a quick escape, draw a weapon etc. Pins like the Ikkyo, Sankyo, or Nikyo pin allow for this. However in a sport context these things are not necessary. So Aikido style pins have unnecessary specialization in MMA.

In armed situations it's very important to control your opponents weapon hand directly, however in unarmed situations this can be done in a much less direct way. Making direct arm control unnecessary in MMA.

In situations where you may need to flee quickly (like his buddy coming to kick you in the head) Aikido style pins work great. There is very little of your body for your opponent to hold in order to slow your escape. In MMA this is unnecessary, you simply hold your opponent until the time elapses, the ref makes you get up, or your opponent quits.

MMA pins are more secure then Aikido pins, but at a cost: lack of good visibility, hard to escape, lack weapon hand control, lack the ability to easily draw your weapon etc. Aikido pins are better non-sport pins, but are not as strong in a controlled environment like sport.